Point-regular covers and sequence-covering compact mappings

Lin, Shou; Ling, Xuewei; Ge, Ying

doi:10.1016/j.topol.2019.106987

Cited by 7 publications

(6 citation statements)

References 14 publications

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“…Since every metrizable space has ωD property [13], Y is strongly Fréchet by Theorem 3.9. Also every strongly Fréchet space which is a closed image of a metric space is metrizable [8,24]. Hence Y is metrizable.…”

Section: Resultsmentioning

confidence: 99%

On ideal sequence covering maps

2019

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<p> In this paper we introduce the concept of ideal sequence covering map which is a generalization of sequence covering map, and investigate some of its properties. The present article contributes to the problem of characterization to the certain images of metric spaces which posed by Y. Tanaka [22], in more general form. The entire investigation is performed in the setting of ideal convergence extending the recent results in [11,15,16]. </p>

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Section: Resultsmentioning

confidence: 99%

On ideal sequence covering maps

2019

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“…In this section, we introduce the concepts of I-cs-networks, I-cs ′ -networks and I-wcs ′ -networks for a space X; and obtain that if X is an J -FU space with a point-countable J -cs ′ -network, then X is a meta-Lindelöf space, for a maximal ideal J of N. 13]). Let I be an ideal on N, X be a topological space and P be a cover of X.…”

Section: On Spaces With I-cs ′ -Networkmentioning

confidence: 99%

On I-quotient mappings and I-cs'-networks under a maximal ideal

Zhou

2020

Appl. Gen. Topol.

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<p>Let I be an ideal on N and f : X → Y be a mapping. f is said to be an I-quotient mapping provided f−1(U) is I-open in X, then U is I-open in Y . P is called an I-cs′-network of X if whenever {xn}n∈N is a sequence I-converging to a point x ∈ U with U open in X, then there is P ∈ P and some n0 ∈ N such that {x, xn0} ⊆ P ⊆ U. In this paper, we introduce the concepts of I-quotient mappings and I-cs′-networks, and study some characterizations of I-quotient mappings and I-cs′- networks, especially J -quotient mappings and J -cs′-networks under a maximal ideal J of N. With those concepts, we obtain that if X is an J -FU space with a point-countable J -cs′-network, then X is a meta-Lindelöf space.</p>

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“…The closure of A in X is denoted by A; moreover, we always denote the set of all the non-isolated points of X by X ′ . For undefined notation and terminologies, the reader may refer to [2], [4], [8] and [19].…”

Section: Notation and Terminologiesmentioning

confidence: 99%